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Cambridge / IGCSE • Algebra

Algebraic Expressions

Algebraic expressions combine numbers, variables, and operation signs. In Grade 8, you build confidence by simplifying expressions and expanding terms.

Learning Objectives

  • Identify terms, coefficients, and variables in expressions
  • Add and subtract polynomials
  • Multiply monomial by polynomial

Lesson Explanation

Lesson Content

An algebraic expression consists of constants (numbers), variables (letters like x, y), and operators (+, -, *). Like terms have the exact same variable part (e.g., 3x and 7x). Only like terms can be added or subtracted together.

💡 Key Takeaway

Take one step at a time, check your working carefully, and keep both sides balanced!

Worked Examples

Example 1

Simplify 5x + 3y - 2x + 7y

  1. Step 1

    Group like terms: (5x - 2x) + (3y + 7y)

  2. Step 2

    Combine x terms: 3x

  3. Step 3

    Combine y terms: 10y

  4. Step 4

    Final simplified expression: 3x + 10y

Example 2

Expand 4(2a - 5b)

  1. Step 1

    Multiply 4 by 2a: 8a

  2. Step 2

    Multiply 4 by -5b: -20b

  3. Step 3

    Final expanded expression: 8a - 20b

Visual Method

Balance Every Step

Mathematics becomes much clearer when you can see the structure behind equations.

Watch Video Explanation

Practice Questions

Try solving each question on paper first. Tap below to check a helpful hint or solution!

Question 1

Simplify 7a + 4b - 3a + 2b

Show Hint / Solution 💡

Group the 'a' terms together and 'b' terms together.

Question 2

Expand 3(4x + 5)

Show Hint / Solution 💡

Multiply 3 by each term inside the bracket.

Question 3

Simplify 2(x + 3) + 4(x - 1)

Show Hint / Solution 💡

Expand both brackets first, then combine like terms.

Lesson Summary

What to Remember

Combine like terms carefully and distribute coefficients across terms inside brackets.

Download Lesson Notes ↓